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Physics > Classical Physics

Abstract: In a recent paper titled "Coherent electromagnetic wavelets and their
twisting null congruences," I defined the local inertia density (I), reactive
energy density (R), and energy flow velocity (v) of an electromagnetic field.
These are the field equivalents of the mass, rest energy, and velocity of a
relativistic particle. Thus R and I are Lorentz-invariant and |v|<=c, with
equality if and only if R=0. The exceptional fields with |v|=c were called
"coherent" because their energy moves in complete harmony with the field,
leaving no inertia or reactive energy behind. Generic electromagnetic fields
become coherent only in the far zone. Elsewhere, their energy flows at speeds
|v|<c. The purpose of this paper is to confirm and clarify this statement by
studying the local energy flow in several common systems: a time-harmonic
electric dipole field, a time-dependent electric dipole field, and a standing
plane wave. For these fields, the energy current (Poynting vector) is too weak
to carry away all of the energy, thus leaving reactive energy in its wake. For
the time-dependent dipole field, we find that the energy can flow both
transversally and inwards, back to the source. Neither of these phenomena show
up in the usual computation of the energy transport velocity which considers
only averages over one period in the time-harmonic case.